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Spinning Conformal Blocks
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For conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the embedding space formalism, we show that one can express all such conformal blocks in terms of simple differential operators acting on the basic scalar conformal blocks. This method gives all conformal blocks for conformal field theories in three dimensions. We demonstrate how this formalism can be applied in a few simple examples.
Forward citations
Cited by 10 Pith papers
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Kontorovich-Lebedev-Fourier Space for de Sitter Correlators
A Kontorovich-Lebedev-Fourier space is built for (d+1)-dimensional de Sitter correlators from the Casimir operator of SO(1,d+1), producing rational propagators and Feynman rules that turn tree and loop diagrams into s...
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CFTs on Squashed Spheres and the Thermal Effective Action
Derives universal quadratic response of 3D CFT free energy to S^3 squashing proportional to c_T and constructs thermal effective action for high-T Seifert manifolds with explicit Wilson coefficients.
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Cosmological Weight-Shifting Matrices
Introduces weight-shifting matrices for de Sitter diagrams, generalized with Kronecker products to arbitrary tree-level graphs, to derive massless wavefunction coefficients from conformally coupled seeds.
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Cosmological Collider in the Grassmannian
Four-point wavefunction coefficients for external conformally coupled scalars exchanging a particle of generic mass and spin are expressed in closed form as hypergeometric functions of Mandelstam invariants times Lege...
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Cosmological Collider in the Grassmannian
The four-point wavefunction coefficient for conformally coupled scalars exchanging a massive spinning particle is written in closed form as a hypergeometric function of the s-channel Mandelstam variable times a Legend...
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Superconformal Weight Shifting Operators
Introduces SU(m,m|2n)-covariant weight-shifting operators in the super-Grassmannian formalism to derive all superconformal blocks from half-BPS ones.
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Spinning bulk-to-boundary correlators in the massless theories with Poincar\'e symmetry
Bulk-to-boundary correlators for spin-s operators in Poincaré-invariant massless theories are linear superpositions of ISO(2)-fixed tensor structures mapped to non-crossing double-line diagrams that are tensor product...
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Thermal conformal partial waves from flat-space and defect CFT
Establishes correspondence between flat, thermal, and defect conformal partial waves via shadow formalism, obtaining thermal blocks from flat four-point and defect two-point functions and reducing the Casimir equation...
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An Alternative Viewpoint on Kinematic Flow from Tubing Splitting
Reversing the direction of tubing evolution yields splitting rules that reproduce the kinematic flow differential equations at tree level and suggest time emerges from kinematic space in conformally coupled scalar mod...
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Notes on Tensor Models and Tensor Field Theories
Lecture notes introducing the 1/N expansion and melonic limit of tensor models, which yield new conformal field theories.
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